Compaction of bi-dispersed granular packing: analogy with chemical thermodynamics

Velocity Profile Geometries and Granular Temperature Distributions in Very Dense Granular Flows

“…The volume fraction ϕ ranges between ϕ RLP ≈ 0.4 for the random loose packing (the lowest ϕ observed in the experiments), and ϕ RCP ≈ 0.64 for the random close packing for ideal spheres. Thus, we can roughly estimate the variation tendency of the Edwards compactivity χ (Edwards & Oakeshott, 1989) according to the relation between χ and ϕ (Chang, 2022; Chang & Deng, 2022; Xia et al., 2015; Yuan et al., 2021), and the result is shown in Figure 4d. The Edwards compactivity represents the dynamic effective temperature of the granular system in the framework of equilibrium statistical physics (Baule et al., 2018; Chang, 2022).…”

“…In this study, we carry out transparent ring‐shear experiments to monitor granular motion over varying shear speeds (0.01–0.5 m/s) under relatively high normal stresses, ranging from 0.1 to 0.5 MPa, frequent in many real geological processes. The velocity fluctuation profile and the volume fraction profile are also obtained, equivalent to the granular kinetic temperature (Goldhirsch, 2008) and the Edwards granular temperature (Chang, 2022; Chang & Deng, 2022; Edwards & Oakeshott, 1989), respectively. Using these data, we try to obtain further insights into the granular dynamics under high‐pressure conditions.…”

Is there a granular potential?

“…Eqn (8) identifies the need for partial molar volumes and entropies that again have analogous functions to those observed in molecular systems, and play important roles in our understanding of mixtures. Chang et al 34 recently took a step in this direction, using partial molar volumes and activity coefficients to describe jamming densities in bi-dispersed granular packings, and Liu et al 51 suggest that a granular potential needs to be developed to understand binary mixtures of confined discs. The granular potential could also play an important role in understanding phase equilibria in granular materials, where we expect both the compactivity and granular potentials to be equal in both phases at coexistence.…”

“…31,32 Less is known with respect to the role a chemical potential plays in dense granular systems that are driven, but move between static, jammed states. A granular chemical potential has been used to study the possibility of a first order phase transition between disordered and crystalline jammed packings in hard spheres 33 and to motivate the use of partial molar volumes in the analysis of bi-disperse granular packings, 34 but more direct investigations of the granular chemical potential are not available.…”

Jamming Density and Volume‐Potential of a Bi‐Dispersed Granular System

“…In order to establish physics laws for particle volume‐potentials, we analyze experimental data for the behavior of partial particle volumes (v 1 or v 2 ) through the following method. Since the volume V of a granular system is an extensive variable, which is homogeneous of degree 1, based on Euler's theorem for homogeneous function (Silbey et al., 2005, Chang & Deng, 2022), the total volume of a mixture can be expressed as $$$V\left({N}_{1},{N}_{2}\right)={N}_{1}\left(\frac{\partial V}{\partial {N}_{1}}\right)+{N}_{2}\left(\frac{\partial V}{\partial {N}_{2}}\right)$$$ …”